Mixing
Proving electrostatic analogy for root locus
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My teacher told us that there is a provable mathematical analogy between root locus and the lines of force generated by electric charges, where every pole can be associated to a positive charge and every zero can be associated to a negative charge.
This sometimes aids is the sketching of the locus when no other rule seems to be of any help (basically using the fact that poles are attracted to the zero that is closer to them, as positive charges do with negative charges).
However I haven't found references to this analogy on the net, thus I was wondering, out of curiosity, how such a relation could be proved: I'd be glad if you could give me some hint on that.
Thank you for your help in advance.
roots control-theory locus
asked Jan 30 at 0:59
LucenLucen
111
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add a comment |
$begingroup$
My teacher told us that there is a provable mathematical analogy between root locus and the lines of force generated by electric charges, where every pole can be associated to a positive charge and every zero can be associated to a negative charge.
This sometimes aids is the sketching of the locus when no other rule seems to be of any help (basically using the fact that poles are attracted to the zero that is closer to them, as positive charges do with negative charges).
However I haven't found references to this analogy on the net, thus I was wondering, out of curiosity, how such a relation could be proved: I'd be glad if you could give me some hint on that.
Thank you for your help in advance.
roots control-theory locus
asked Jan 30 at 0:59
LucenLucen
111
$endgroup$
1
$begingroup$
I am not sure if this is actually true. For example when you put the poles and zeros onto a straight line the root locus plot does not have to stay on that line, while it should for static charges. Unless maybe they have some initial velocity.
$endgroup$
– Kwin van der Veen
Jan 30 at 5:43
add a comment |
$begingroup$
My teacher told us that there is a provable mathematical analogy between root locus and the lines of force generated by electric charges, where every pole can be associated to a positive charge and every zero can be associated to a negative charge.
This sometimes aids is the sketching of the locus when no other rule seems to be of any help (basically using the fact that poles are attracted to the zero that is closer to them, as positive charges do with negative charges).
However I haven't found references to this analogy on the net, thus I was wondering, out of curiosity, how such a relation could be proved: I'd be glad if you could give me some hint on that.
Thank you for your help in advance.
roots control-theory locus
asked Jan 30 at 0:59
LucenLucen
111
$endgroup$
My teacher told us that there is a provable mathematical analogy between root locus and the lines of force generated by electric charges, where every pole can be associated to a positive charge and every zero can be associated to a negative charge.
This sometimes aids is the sketching of the locus when no other rule seems to be of any help (basically using the fact that poles are attracted to the zero that is closer to them, as positive charges do with negative charges).
However I haven't found references to this analogy on the net, thus I was wondering, out of curiosity, how such a relation could be proved: I'd be glad if you could give me some hint on that.
Thank you for your help in advance.
roots control-theory locus
roots control-theory locus
asked Jan 30 at 0:59
LucenLucen
111
asked Jan 30 at 0:59
LucenLucen
111
asked Jan 30 at 0:59
LucenLucen
111
asked Jan 30 at 0:59
LucenLucen
111
asked Jan 30 at 0:59
LucenLucen
111
111
1
$begingroup$
I am not sure if this is actually true. For example when you put the poles and zeros onto a straight line the root locus plot does not have to stay on that line, while it should for static charges. Unless maybe they have some initial velocity.
$endgroup$
– Kwin van der Veen
Jan 30 at 5:43
add a comment |
1
$begingroup$
I am not sure if this is actually true. For example when you put the poles and zeros onto a straight line the root locus plot does not have to stay on that line, while it should for static charges. Unless maybe they have some initial velocity.
$endgroup$
– Kwin van der Veen
Jan 30 at 5:43
1
1
$begingroup$
I am not sure if this is actually true. For example when you put the poles and zeros onto a straight line the root locus plot does not have to stay on that line, while it should for static charges. Unless maybe they have some initial velocity.
$endgroup$
– Kwin van der Veen
Jan 30 at 5:43
$begingroup$
I am not sure if this is actually true. For example when you put the poles and zeros onto a straight line the root locus plot does not have to stay on that line, while it should for static charges. Unless maybe they have some initial velocity.
$endgroup$
– Kwin van der Veen
Jan 30 at 5:43
add a comment |
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I am not sure if this is actually true. For example when you put the poles and zeros onto a straight line the root locus plot does not have to stay on that line, while it should for static charges. Unless maybe they have some initial velocity.
$endgroup$
– Kwin van der Veen
Jan 30 at 5:43